Experiment #1 Kinematics of Rotational Motion

Method 1

θ = θ0 + ω0t + .5αt2
α = .3397 rad/sec^2

Method 2

Vertical Displacement = .69 m
a = αr
a = .0075 m/s^2
Pulley radius = .0225
α = a/r
α = .32

.32/.3397 = 94.2% The acceleration values agree within the uncertainty of measurement.

Experiment #2

Method 1

Angular acceleration of rotating apparatus = .3397 rad/s^2
Linear Acceleration of falling mass = .0075 m/s^2
Radius of pulley = .0225
Falling mass (m) = .23 kg
Ft = (.23)(.0075) = T - (.23)(9.8)
Ft = 2.256
I = .0225(2.256)/(.3397)
I = .1494 kg * m^2

Method 2

I(pulleys) = .00058 kg m^2
Thin Rods: length = .3625 m, mass = 74.105 kg
I (thin rods) = .003246 kg * m^2 (times four) = .012984 kg*m^2
Moveable mass: mass = .184 kg distance from center = .3525 m
I (moveable mass) = .02295 (times four) = .091791 kg*m^2
I = .00058 + .012984 + .091791 = .105355 kg*m^2

(.1494 - .105355)/((.1494 + .105355)/2) * 100 = 34.58% Error, so they are not too different

Experiment #3

Gravitational Potential Energy

Mass = .230 kg
Vertical displacement = 1 m
PE = 2.254 J

Translational Kinetic Energy

t (average) = 14.5 sec
v (average) = .06897 m/s
v (final) = .1379 m/s
KE = .02188 J

Rotational Kinetic Energy

Radius of pulley = .0225 m
w (final) = 6.1289 rad/s
I = .105355 kg*m^2
KE = 1.9788 J

KE (total) = .002188 + 1.9788 = 1.981 J
Error = 12.896%
The main reason for the difference is friction and human error (not percise measurement).